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# Copyright (c) 1997-2018
# Ewgenij Gawrilow, Michael Joswig (Technische Universitaet Berlin, Germany)
# http://www.polymake.org
#
# This program is free software; you can redistribute it and/or modify it
# under the terms of the GNU General Public License as published by the
# Free Software Foundation; either version 2, or (at your option) any
# later version: http://www.gnu.org/licenses/gpl.txt.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#-------------------------------------------------------------------------------
object Action {
# @category Symmetry
# The generators of the group action
property GENERATORS : Array<GeneratorType>;
# @category Symmetry
# The degree of the representation. For permutation groups,
# this is the number of permuted indices, for matrix groups
# it is the dimension of the vector space the group acts on
property DEGREE : Int;
# @category Symmetry
# The character of the action. The ordering corresponds to the
# columns of the CHARACTER_TABLE
property CHARACTER : Array<QuadraticExtension>;
# @category Symmetry
# The multiplicities of each irreducible representation in this action.
# The ordering corresponds to the rows of the CHARACTER_TABLE
property IRREDUCIBLE_DECOMPOSITION : Array<Int>;
# @category Symmetry
# A set of representatives for each conjugacy class.
# The order of these representatives must agree with the implicit
# order of the columns of the [[Group::CHARACTER_TABLE|CHARACTER_TABLE]].
property CONJUGACY_CLASS_REPRESENTATIVES : Array<GeneratorType>;
# @category Symmetry
# The conjugacy classes themselves
property CONJUGACY_CLASSES : Array<Set<GeneratorType>>;
# @category Symmetry
# All elements of the group, as expressed in the present action
# Notice that this is a temporary property; it will not be stored in any file.
property ALL_GROUP_ELEMENTS : Array<GeneratorType>;
rule ALL_GROUP_ELEMENTS : GENERATORS {
$this->ALL_GROUP_ELEMENTS(temporary) = all_group_elements($this);
}
# @category Symmetry
# the name of the property that we act on, for example MAX_INTERIOR_SIMPLICES or INTERIOR_RIDGES
property DOMAIN_NAME : String;
# @category Symmetry
# the name of a different action that this action is induced from
property INDUCED_FROM : String;
# @category Symmetry
# The map giving the index of each group element
# This is a temporary property; it will not be stored in any file.
property INDEX_OF : HashMap<DomainType, Int>;
rule INDEX_OF : DOMAIN_NAME {
my $dom = $this->DOMAIN_NAME;
$this->INDEX_OF(temporary) = index_of($this->$dom);
}
# @category Symmetry
# The orbits of the domain, represented via their indices
property ORBITS : Array<Set<Int>>;
# @category Symmetry
# The number of orbits in the domain under the group action
property N_ORBITS : Int;
# @category Symmetry
# The cardinality of each orbit
property ORBIT_SIZES : Array<Int>;
# @category Symmetry
# The images of all domain elements under each group element: [ [ g(x) for x in D ] for g in G ]
property IMAGES : Array<Array<DomainType>>;
# @category Symmetry
# A set of generators for input rays, stored as the rows of a matrix.
# The list of generators may be redundant and non-canonical.
property INPUT_RAYS_GENERATORS : Matrix<OrbitGeneratorScalarType>;
# @category Symmetry
# The number of generators for orbits.
property N_INPUT_RAYS_GENERATORS : Int;
# @category Symmetry
# A set of generators for rays, stored as the rows of a matrix.
# The list of generators may be redundant and non-canonical.
property RAYS_GENERATORS : Matrix<OrbitGeneratorScalarType>;
# @category Symmetry
# The number of generators for orbits.
property N_RAYS_GENERATORS : Int;
# @category Symmetry
# A set of generators for inequalities, stored as the rows of a matrix.
# The list of generators may be redundant and non-canonical.
property INEQUALITIES_GENERATORS : Matrix<OrbitGeneratorScalarType>;
# @category Symmetry
# The number of generators for orbits.
property N_INEQUALITIES_GENERATORS : Int;
# @category Symmetry
# A set of generators for facets, stored as the rows of a matrix.
# The list of generators may be redundant and non-canonical.
property FACETS_GENERATORS : Matrix<OrbitGeneratorScalarType>;
# @category Symmetry
# The number of generators for orbits.
property N_FACETS_GENERATORS : Int;
# @category Symmetry
# A set of generators for equations, stored as the rows of a matrix.
# The list of generators may be redundant and non-canonical.
property EQUATIONS_GENERATORS : Matrix<OrbitGeneratorScalarType>;
# @category Symmetry
# The number of generators for orbits.
property N_EQUATIONS_GENERATORS : Int;
# @category Symmetry
# A set of generators for input lineality, stored as the rows of a matrix.
# The list of generators may be redundant and non-canonical.
property INPUT_LINEALITY_GENERATORS : Matrix<OrbitGeneratorScalarType>;
# @category Symmetry
# The number of generators for orbits.
property N_INPUT_LINEALITY_GENERATORS : Int;
# @category Symmetry
# A set of generators for input lineality, stored as the rows of a matrix.
# The list of generators may be redundant and non-canonical.
property LINEALITY_SPACE_GENERATORS : Matrix<OrbitGeneratorScalarType>;
# @category Symmetry
# The number of generators for orbits.
property N_LINEALITY_SPACE_GENERATORS : Int;
# @category Symmetry
# A set of generators for the maximal cones of a fan, stored in terms of indices of vertex generators.
# The list of generators may be redundant and non-canonical.
property MAXIMAL_CONES_GENERATORS : IncidenceMatrix;
# @category Symmetry
# The number of generators for orbits.
property N_MAXIMAL_CONES_GENERATORS : Int;
# @category Symmetry
# A collection of representatives for each orbit, represented via their indices
property ORBIT_REPRESENTATIVES : Array<Int>;
# @category Symmetry
# Labels for the orbit representatives
property ORBIT_REPRESENTATIVE_LABELS : Array<String> : mutable;
# @category Symmetry
# the representatives of orbits explicitly, not via their indices
property EXPLICIT_ORBIT_REPRESENTATIVES : Array<DomainType>;
# @category Symmetry
# the representatives of orbits explicitly, not via their indices
property EXPLICIT_ORBIT_REPRESENTATIVE_MATRIX : Matrix<OrbitGeneratorScalarType>;
# @category Symmetry
# the number of representatives of orbits
property N_ORBIT_REPRESENTATIVES : Int;
# @category Symmetry
# A permutation that orders the domain elements by orbits
property PERMUTATION_TO_ORBIT_ORDER : Array<Int>;
}
# Local Variables:
# mode: perl
# cperl-indent-level:3
# indent-tabs-mode:nil
# End:
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